Parallel Ion Flow Research Articles

Ion dynamics in helicon sources

Recent experiments have demonstrated that phenomena associated with ion dynamics, such as the lower hybrid resonance, play an important role in helicon source operation. In this work, a review of recent ion heating measurements and the role of the slow wave in heating ions at the edge of helicon sources is presented. The relationship between parametrically driven waves and ion heating near the rf antenna in helicon sources is also discussed. Recent measurements of parallel and rotational ion flows in helicon sources are presented and the implications for particle confinement, instability growth, and helicon source operation are reviewed.

Numerical modeling of linear drift-tearing mode stability

Numerical modeling results of the linear drift tearing modes are presented. The present model is based on the two-fluids equations, and the perturbed bootstrap current is also included. The electron temperature and the density perturbations are self-consistently calculated by solving the two-dimensional transport equations. It is found that, with the inclusion of the electron perpendicular heat transport, which is neglected in the previous theory, the behavior of the drift tearing mode becomes significantly different, and a new type of tearing mode instability appears. This mode is driven unstable by a sufficiently large electron temperature gradient in a certain range of the electron diamagnetic drift frequency ω*e. The stability of the drift tearing mode is found to be mainly determined by ω*e. The parallel ion flow driven by the parallel pressure gradient is found to be stabilizing for the drift tearing modes, while the perturbed bootstrap current is destabilizing for large or small ω*e but can be stabilizing for a certain range of ω*e.

Linear Analysis of Neoclassical Tearing Mode based on the Four-Field Reduced Neoclassical MHD Equation

The linear neoclassical tearing mode is investigated using the four-field reduced neoclassical MHD equations, in which the fluctuating ion parallel flow and ion neoclassical viscosity are taken into account. The dependences of the neoclassical tearing mode on collisionality, diamagnetic drift and q profile are investigated. These results are compared with the results from the conventional three-field model. It is shown that the linear neoclassical tearing mode is stabilized by the ion neoclassical viscosity in the banana regime even if Δ'>0.

Effects of poloidal variation of neutral density on Pfirsch–Schlüter transport near the tokamak edge

Effects of neutral particles on plasma flows and radial transport in a collision-dominated plasma are discussed, with a particular attention given to the modifications due to a poloidal variation of the neutral density. It is found that neutrals are of no importance if the radial particle transport is on a Pfirsch–Schlüter level. If, on the other hand, anomalous effects increase this transport to the Pfirsch–Schlüter radial heat transport level or higher, neutral effects become important in determining the radial heat transport, radial electric field, and the ion parallel flow velocity.

On the role of ion temperature anisotropy in the growth and propagation of shear‐modified ion‐acoustic waves

Oblique ion‐acoustic waves, excited by the combination of magnetic field‐aligned (parallel) electron drift and sheared parallel ion flow, are investigated in magnetized laboratory plasma that is characterized by ion temperature anisotropy. Direct measurements of the parallel and perpendicular ion temperatures, parallel and perpendicular ion drift velocities, electron temperature and parallel electron drift velocity, parallel and perpendicular wave vector components, and mode frequency and growth rate are used to elucidate the shear‐modified ion‐acoustic (SMIA) instability mechanism and document an observed correlation between ion temperature anisotropy and wave propagation angle. Experimental measurements show that anisotropy significantly influences the growth rate and propagation angle of oblique ion‐acoustic waves. These results support the ion‐acoustic wave interpretation of broadband waves in the auroral energization region where shear and anisotropy are known to exist and may have ramifications for many space plasmas in which anisotropy exists in the electron temperature or ion temperature.

Observation of inverse ion-cyclotron damping induced by parallel-velocity shear.

The generation of broadband multiharmonic spectra of electrostatic ion-cyclotron waves is demonstrated in a magnetized laboratory plasma in which shear in the magnetic-field-aligned (parallel) ion flow and a relative parallel electron drift are present. Shear correlates with an increased number of harmonics and a decreased electron drift speed. Wave and particle measurements indicate that cyclotron damping is reduced and even becomes negative. The fluctuations in the time domain are spiky, similar to electric-field fluctuations observed both in Earth's auroral zone and in numerical simulations.

Low frequency oscillations in a plasma with spatially variable field-aligned flow

The effects of a transverse gradient in the plasma flow velocity parallel to the ambient magnetic field are analyzed. A transverse velocity gradient in the parallel ion flow, even in small magnitude, can increase the parallel phase speed of the ion-acoustic waves sufficiently to reduce ion Landau damping. This results in a significantly lower threshold current for the current driven ion acoustic instability. Ion flow gradients can also give rise to a new class of ion cyclotron waves via inverse cyclotron damping. A broadband wave spectrum with multiple cyclotron harmonics is possible. A combination of the multiple cyclotron harmonic waves can result in spiky electric field structures with their peaks separated by an ion cyclotron period. A spatial gradient in the parallel electron flow is also considered but it is found to play a minimal role in the low frequency regime. Relevance of these to natural plasma environments is discussed.

Electrostatic potential and plasma flow near the edge of a divertor tokamak

Explicit expressions are given to determine the electrostatic potential and ion parallel flow velocity in the region of an axisymmetric low collisionality tokamak with moderately large ion flow, electrostatic potential, and safety factor Q.

Effect of the inductive electric field on ion flow in tokamaks

The effect of the inductive electric field of a tokamak on the parallel (and poloidal) ion flow in the banana regime is evaluated. It is demonstrated that the flow is in the direction of the parallel current and is surprisingly large—comparable to the usual banana regime ion temperature gradient drive.

A new f method for neoclassical transport studies

A new f method is presented in detail to solve the drift kinetic equation for the simulation study of neoclassical transport. It is demonstrated that valid results essentially rely on the correct evaluation of the marker density g in the weight calculation. A new weighting scheme is developed without assuming g in the weight equation for advancing particle weights, unlike previous schemes. This scheme employs an additional weight function to directly solve g from its kinetic equation based on the f method itself. Therefore, the severe constraint that the real marker distribution must be consistent with the initially assumed g is relaxed. An improved like-particle collision scheme is also presented. By compensating for momentum, energy and particle losses, the conservations of all three quantities are greatly improved during collisions. With the improvement in both the like-particle collision scheme and the weighting scheme, the f simulation shows a significantly improved performance. The new f method is applied to the study of ion neoclassical transports due to self-collisions, taking the effect of finite orbit width into account. The ion thermal transport near the magnetic axis is shown to be greatly reduced from its conventional neoclassical level, like that of previous f simulations. On the other hand, the direct particle loss from the confinement region may strongly increase the ion thermal transport near the edge. It is found that the ion parallel flow near the axis is also largely reduced due to non-standard orbit topology.

Spectroscopic measurements of impurity temperatures and parallel ion flows in the DIII-D divertor

Impurity ion temperatures and parallel flow velocities in the DIII-D divertor have been measured from the shapes and shifts of visible spectral lines of C II, C III, and B II. Spectral multiplet patterns are analyzed by fitting them to theoretical profiles that incorporate exact calculations for the Zeeman/Paschen-Back effect. Both normal flows toward the target plate and reversed flows away from the target plate are observed in the outer divertor leg; only flows toward the plate are detected in the inner leg.

Neutral diffusion and anomalous effects on collisional ion flow shear in tokamaks

Ion plasma flow and flow shear just inside the last closed flux surface of a tokamak can be strongly altered by neutral atoms and anomalous effects. For a collisional edge, neutrals modify the standard Pfirsch–Schlüter expression for the parallel ion flow through the strong coupling provided by ion–neutral collisions. Even for rather small neutral to plasma density ratios, the large diffusivity of the neutrals in combination with the ion–neutral coupling can directly modify the ion distribution function as well as cause neutral diffusion modifications to the parallel momentum constraint that determines the parallel ion flow. Direct modification of the ion distribution function only dominates at order unity aspect ratios, and was unimportant in an earlier plateau evaluation of the effects of neutrals on ion flow. Like the earlier work, anomalous effects are retained to maintain a steady state and demonstrate that large anomalous transport can alter neoclassical collisional ion flows.

Neutral diffusion and anomalous effects on ion flow shear

Bulk ion flow can be modified by ion–neutral interactions in the edge region of tokamaks where neutral atoms are abundant. In this region, the standard neoclassical expression for the ion flow is not consistent with the experimental observations. Previous work in the plateau regime [Valanju et al., Phys. Fluids B 4, 2675 (1992)] suggests that the discrepancy is caused mainly by momentum loss due to ion–neutral charge exchange. In the present work we show that in the absence of neutral diffusion, charge exchange cannot affect the neoclassical transport of the ions significantly if the neutral mean-free path is short and the neutral density is low compared to the plasma density. However, the inclusion of neutral diffusion and anomalous processes in the plateau regime can substantially modify parallel ion flow inside the separatrix as determined by the flux surface averaged momentum constraint. Moreover, the local shear in the flow may be determined by a balance between neutral diffusion and anomalous effects which may then modify the turbulent transport.

Experimental study of the collisional parallel velocity shear instability

Simultaneous density and electric field fluctuation spectra, associated with velocity shear (both in the transverse to the magnetic field ion flow velocity and in the parallel ion flow velocity), have been observed by the DE 2 spacecraft in the F region [Basu et al., 1984]. Basu and Coppi [1988, 1989] argued that the subkilometer scale irregularities are due to collisional electrostatic modes excited in a partially ionized plasma in the presence of shear in the parallel ion flow. In this paper we describe results of a laboratory investigation of the effects of neutral‐particle collisions on the parallel velocity shear instability, performed using a double‐ended Q machine. The critical value of the shear dv0/dx, the derivative of the field‐aligned ion flow with respect to the transverse (to B) coordinate, is determined and compared with theoretical predictions.

Tokamak Edge Transport Theory

AbstractKinetic equations commonly used to study the plasma core of a tokamak do not allow a balance between parallel ion streaming and radial diffusion and are, therefore, inappropriate in the plasma edge. Standard core tokamak transport orderings allow large divergence‐free flows in flux surfaces, but only weak radial flows. Alternate orderings are required in the edge region where radial diffusion must balance large parallel ion flows to divertor target plates or limiters. Similarly, core transport formulae cannot be extended to the edge region without qualitative alteration. Here we address the necessary changes by considering a large parallel flow ordering appropriate for the scrape‐off layer of a tokamak. By deriving and solving a novel kinetic equation, we construct distinctive transport laws for an impure, collisional edge plasma. We find in particular a surprising form for parallel transport in the scrape‐off layer, in which the parallel flow of particles (and heat) are driven by a combination of the conventional gradients, as well as viscosity terms and new terms involving products of radial derivatives of the parallel mean velocity with density and temperature gradients. The new terms are not relatively small, and could affect understanding of limiter and divertor operation.

Poloidal rotation in tokamaks with large electric field gradients

The ion poloidal flow velocity near the plasma edge in a tokamak has been calculated by extending neoclassical theory to include orbit squeezing, which is the reduction of the ion banana widths due to radial electric field shear. The pressure gradient-driven ion parallel flow is reduced by orbit squeezing, and then no longer cancels the diamagnetic flow in its contribution to poloidal flow. This allows the poloidal flow velocity to be a significant fraction of the ion diamagnetic velocity, which can be much larger than the standard neoclassical value (proportional to the ion temperature gradient). Equations for determining the poloidal flow and radial electric field profiles self-consistently are given.

Bifurcations and modulational interaction in negative compressibility turbulence

The results of detailed numerical studies of phenomena in negative compressibility turbulence with sheared perpendicular (i.e., poloidal) flow are presented. The turbulence model is based on the parallel ion flow gradient instability, a representative paradigm for ion drift waves. Studies of coupled turbulence and mean flow evolution indicate the existence of two distinct nonlinear states. In the first state, saturation occurs via nonlinear transfer to damped high-k modes and sheared flow is heavily damped. In the second state, the turbulence level is controlled by the self-consistently generated sheared flow. Transition between these states is determined by the competition between instability growth and damping of rotation. The dynamics of the observed transition is well described and consistent with a simple set of coupled envelope equations. Modulational interaction between small scale turbulence and large scale m≠0 shear flows is observed, as well.

Galileo observations of the motions of ion and electron plasmas in the magnetotail

We report the first fully three‐dimensional determinations of the bulk motions of ion and electron plasmas in Earth's magnetotail at geocentric radial distances near the lunar orbit. The two regions that are examined are the plasma sheet and the plasma mantle. The magnitudes and directions of the bulk velocities are the same for the ion and electron plasmas in the plasma mantle. However, in the plasma sheet the electron bulk speeds are often substantially greater than the ion bulk speeds. This situation arises because the component of electron flow along the magnetic field is greater than the ion parallel flow. Most of the bulk flow of the electrons is often attributable to the presence of field‐aligned currents, not E × B convection of plasmas. Hence previously reported two‐dimensional electron velocity distributions do not give a reliable determination of mass transport and convection in the plasma sheet at these distances in the magnetotail.

Ion-temperature-gradient-driven modes in neoclassical regime

A reduced set of neoclassical fluid equations, consisting of the parallel ion flow velocity v∥, the generalized potential F, the ion pressure p, and the parallel ion heat flow q∥, is derived. The resultant equations are the extension of reduced fluid equations derived from Braginskii equations with the high collisionality to the equations relevant to a fusion plasma with low to intermediate collisionality. The linear ηi mode dynamics is reinvestigated by using the resultant model equations. The effects of the perpendicular compressibility in the ion pressure response, the parallel heat flow, and the neoclassical viscosity are analyzed both analytically and numerically. It is stressed that the closure condition of neoclassical viscosity changes the sign of energy dissipation and seriously affects the stability of ηi modes.

Effects of Fast Ions and an External Inductive Electric Field on the Neoclassical Parallel Flow, Current and Rotation in General Toroidal Systems.

Effects of external momentum sources, i.e., fast ions produced by the neutral beam injection and an external inductive electric field, on the neoclassical ion parallel flow, current, and rotation are analytically investigated for a simple plasma in general toroidal systems. It is shown that the contribution of the external sources to the ion parallel flow becomes large as the collision frequency of thermal ions increases because of the momentum conservation of Coulomb collisions and sharply decreasing viscosity coefficients with collision frequency. As a result, the beam-driven parallel flow of thermal ions becomes comparable to that of electrons in the Pfirsh-Schluter collisionality regime, whereas in the 1/ν or banana regime it is smaller than that of electrons by the order of √me/mi (me and mi are electron and ion masses). This beam-driven ion parallel flow can not produce a large beam-driven current because of the cancellation with electron parallel flow, but produces a large toroidal rotation of ions.As both electron and ions approach the Pfirsh-Schluter collisionality regime the contribution of thermodynamical forces becomes negligibly small and the large toroidal rotation of ions is predominated by the beam-driven component in the non-axisymmetric configuration with large helical ripples.